Hence, the relaxation model predicts the formation of an exponentially localized domain wall with the profile \(u(y) = \psi (y/l_\phi )\) , such that the characteristic width \(\lambda _\phi \)  is smallest for a shear
boundary (interlayer translation \(R_\phi \Delta \mathbf {b}\)  parallel to the domain wall) with \(l_\perp = \sqrt{\frac{\mu }{2 k_\textrm {min}}} \Vert \Delta \mathbf {b}\Vert \) , and largest for a tensile boundary (interlayer translation orthogonal to the domain wall) with \(l_\parallel = \sqrt{\frac{\lambda + 2\mu }{2 k_\textrm {min}}} \Vert \Delta \mathbf {b}\Vert \) . This behavior matches experimental observationsNote that in [1]} the GSFE profile across the domain wall is approximated by the sine-Gordon potential \(\Phi (\Delta u) = \frac{V_\textrm {SP}}{2} (1 - \cos (2\pi \Delta u))\)  for \(0 \le \Delta u \le 1\)  allowing for an explicit solution, and a different normalization was used with \(k = \Phi [0] - \Phi _\textrm {min}\)  the saddle point energy, resulting in a slightly different expression for the thickness of the domain wall.
